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| File | Description | Size | Format | |
|---|---|---|---|---|
| Lectures_in_Mathematics_12.pdf | 14.88 MB | Adobe PDF | View/Open |
| Title: | Theory of group characters |
| Authors: | Brauer, Richard |
| Keywords: | Characters of groups |
| Issue Date: | 1979 |
| Publisher: | Kinokuniya |
| Journal title: | Lectures in Mathematics |
| Volume: | 12 |
| Table of contents: | I. Preliminaries §1. Algebras and their representations [1-8] §2. Representations of finite groups - classical theory [8-19] §3. Cyclotomic splitting fields [19-30] II. Arithmetical Structure §1. The numbers ω_i(K_α) [31] §2. Modular representations and their characters [32-33] §3. Transition from an ordinary representation to a modular one [33-34] §4. Decomposition numbers and Cartan invariants [34-37] §5. The number of irreducible modular characters [37-39] §6. The chacacters Φ_⍴ [39-41] §7. The p-rank of the matrix D of decomposition numbers [41-43] §8. Blocks [43-46] §9. Idempotents belonging to blocks [46-50] §10. Defect of a block [50-52] §11. The determinant of the matrix C of Cartan invariants [52-56] §12. The elementary divisors of C and C_τ [56-63] §13. The number of irreducible characters in a block [63-66] III. Defect groups. Main theorem A §1. Blocks of G and those of subgroups [67-71] §2. Defect groups of a block [71-78] §3. Main Theorem A [78-81] IV. Generalized Decomposition Numbers, Main Theorem B §1. Generalized decomposition numbers [82-84] §2. Sections [84-88] §3. The matrix of generalized decomposition numbers [88-92] §4. Main Theorem B [93] §5. Some consequences [93-104] References [104-107] |
| Description: | Notes prepared by T. Tsuzuku, in cooperation with T. Nakayama, P. Fong, A. Mizutani, N. Ito |
| URI: | http://hdl.handle.net/2433/84917 |
| Appears in Collections: | Lectures in Mathematics : Department of Mathematics, Kyoto University |
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